The Structural Peculiarities of Statistical Interrelationships in Econometric Analysis of Multivariate Sample Data: An Overview and Methodical Recommendations for Students

Abstract

The general theory in economics is largely descriptive; therefore, its mathematical models are not only statistical but also particular. In the study of economic phenomena, it is usually necessary to use particular methods and thereby receive only particular solutions. Particular conditions limit the application of such methods, for example, types of economic activities and their place and time of implementation. The general solution to a mathematical problem allows for obtaining a particular solution of almost any initial and boundary conditions. In contrast to the general methods of mathematics, under which we find general solutions to whole classes of problems, in economics, solutions are always particular. We can only reach a true understanding of the character of the economic phenomenon that interests us through statistical data analysis. Correlation analysis is a time-consuming and completely nonformalizable task, necessary for identifying the dynamic of relationships between a large number of factors. Additionally, the nature of statistical models used for obtaining the sample estimates of parameters predetermines the quality and interpretation of the results of statistical analysis. Due to the complexity of multivariate statistical models, the assumption that the sample data follow a multidimensional normal distribution usually limits the common theoretical view. This greatly assists in performing standard multivariate analysis but always leads to a linear regression. The result is an oversimplified model of the correlations that develop in real conditions. The economic structure of each object is unique. Therefore, we propose to illustrate it with a system of correlation matrices of different orders. We propose that the synthesis of large quantities of multivariate sample data via snapshots of correlation matrices visually represents the specific features of the object of study. Employing such snapshots converts the empirical system of statistically significant relationships to the desired model of economic relationships. We establish the preconditions for the practical use of the generic methods of system analysis, based on modern theoretical and software tools.